Since the discovery of an “unusual hemoglobin in patients with diabetes,” over 40 years ago1, Hemoglobin A1c (HbA1c) has become the established standard clinical measurement used as a marker for glycemic control. HbA1c is formed when hemoglobin joins with glucose in the blood, resulting in a glycosylated hemoglobin molecule. Due to the fact that red blood cells survive for 8-12 weeks before renewal, a patient's HbA1c reflects the average blood glucose levels over the past 3 months.
The widespread acceptance of this measurement has primarily been driven by two pivotal, large-scale studies in Type 1 (Diabetes Control and Complications Trial; DCCT) and Type 2 (UK Prospective Diabetes Study; UKPDS) diabetes. These prospective, randomized, controlled trials of intensive versus standard glycemic control in patients with relatively recently diagnosed diabetes demonstrated that intensive glucose control, as measured by blood glucose and HbA1c, correlated with a decreased risk of diabetes-related complications2,3. The DCCT and UKPDS, along with other clinical studies, also have been used to support the development of hypothetical scenarios and test mathematical calculation models which aim to describe the relationship between HbA1c and blood glucose.
Linear Models for Blood Glucose-HbA1c Relationship
Based on the UKPDS in type 2 diabetes (T2D) patients a linear regression relationship of HbA1c with fasting plasma glucose (FPG) was observed, where FPG=1.28 (HbA1c)−0.66 (r2=0.59).4 Similarly, using data from the DCCT in type 1 diabetes (T1D) patients, Rohlfing et al. analyzed 26,056 values based on 7 mean blood glucose (MPG) measures per day.5 Using this approach, they established a linear relationship between plasma glucose and HbA1c (MPG (mmol/l)=(1.98× HbA1c)−4.29 or MPG (mg/dl)=(35.6×HbA1c)−77.3; r=0.82). This was subsequently used for the American Diabetes Association (ADA) Standards of Medical Care in Diabetes to describe the correlation between HbA1c and mean glucose. However, in the most recent update, it is now considered that this was not optimal, being derived from relatively sparse data (one 7-point profile over 1 day per HbA1c reading) in the primarily Caucasian T1D participants of the DCCT.6 
More recently, the ADAG Study Group evaluated data from T1D, T2D and Non-Diabetic patients using self-monitored blood glucose (SMBG).7 The aim was to define a relationship between HbA1c and average glucose (AG) levels and determine whether HbA1c could be expressed and reported as AG in the same units as used in self-monitoring. Approximately 2,700 glucose values were obtained for each subject during 3 months. Linear regression between the HbA1c and AG values provided the closest correlations, allowing for calculation of an estimated average glucose (eAG) for HbA1c values using the formula AG (mg/dl)=28.7*A1c−46.7; r2=0.84; P<0.0001. Furthermore the authors found that the linear regression equations did not differ significantly across sub-groups based on age, sex, diabetes type, race/ethnicity, or smoking status. This has now been adopted as the current recommended relationship to use according to the ADA 2011 Standards of Medical Care in Diabetes.6 
Makris, et al have also observed a similar data pattern, with a strong correlation seen between MBG and HbA1c in Type 2 diabetic patients, using the formula MBG (mg/dl)=(34.74*HbA1c)−79.21 or MBG (mmol/l)=1.91*HbA1c−4.36; r=0.93. They also found that the linear regression of MBG values vs. HbA1c at 12 weeks was statistically significant; whereas other independent variables of sex, age, body mass index (BMI) and patient status (Type 2 diabetes treated or not) were not.8 Temsch et al also identified issues with a linear mathematical model developed to calculate HbA1c values based on SMBG and past HbA1c levels (HbA1c=2.6+0.03*G [mg/100 ml] or 2.6+0.54*G [mmol/l]). Overall, the predicted HbA1c values were consistent with measured values and results matched the HbA1c formula in the elevated range. However, the model was found to be too optimistic in the range of better glycemic control. Sub-analysis suggested that bias may have been introduced by use of different glucometers and individual measurement habits.9 
Factors Influencing the Relationship Between Blood Glucose and HbA1c
A range of factors have been postulated to influence the relationship HbA1c and blood glucose, such as patient's age, body weight (BMI), gender, ethnicity, behavioral characteristics (e.g. time and frequency of blood glucose measurement) and their general status such as duration and type of diabetes, concomitant diseases, etc.10,11,12,13. In particular, two critical areas have been identified which appear to have significant impact on this relationship:
1) The time of blood glucose measurement (fasting (FPG), post-prandial etc.) and
2) The frequency and timing of blood glucose measurement.
Whilst postprandial hyperglycemia, like preprandial hyperglycemia, contributes to elevated HbA1c levels, its relative contribution is higher at HbA1c levels that are closer to 7%. However, the major outcome studies such as the DCCT and UKPDS, relied overwhelmingly on pre-prandial SMBG. Analysis of DCCT found that among individual time points, the afternoon and evening prandial glucose (post-lunch, pre-dinner, post-dinner, and bedtime) readings showed higher correlations with HbA1c than the morning time points (pre-breakfast, post-breakfast, and pre-lunch), with the best correlation of HbA1c being the area under the glucose profile.14 Yamamoto-Honda et al also showed that FPG and 2-h post-breakfast blood glucose (PBBG) levels exhibited a good sensitivity and specificity for predicting a glycemic control, while the FPG and 3-h PBBG levels only exhibited fair sensitivity and specificity for predicting glycemic control.15 Similarly chronology and frequency of blood glucose measurements also has influence on the relationship between blood glucose and HbA1c. At any given time, a given blood sample contains erythrocytes of varying ages, with different levels of exposure to hyperglycemia. Whilst the older erythrocytes are likely to have more exposure to hyperglycemia, younger erythrocytes are more numerous. Blood glucose levels from the preceding 30 days contribute approximately 50% to HbA1c, whereas those from the period 90-120 days earlier contribute only approximately 10%.16 Exploiting further the timing of blood glucose measurements, Trevino challenged the linear model approach as fundamentally flawed and had instead pursued weighted average and nonlinear approaches.17,18,19 
Development of Non-Linear Models for Blood Glucose-HbA1c Relationship
Several nonlinear models have been proposed, which aim to address additional key factors that influence the relationship between blood glucose and HbA1c. Zielke et al proposed that HbA1c values reflect serum glucose levels of the immediate past much better than levels several weeks ago. Using a biomathematical model that takes into account the chemical reactions during HbA1c formation as well as the life cycle of human erythrocytes, they concluded that in order to ensure some degree of reliability of HbA1c measurements, these readings should not be spaced too far apart.20 Ollerton et al developed an approach to address the relative contribution of fasting and post-prandial glucose levels to the value of HbA1c, using a mathematical model of hemoglobin glycation. They highlighted that this is based on physiologically reasonable assumptions, to derive a compartmental differential equation model for HbA1c dynamics.21 Other groups have used data from clinical studies (including DCCT) and hypothetical scenarios, to propose models which incorporate the kinetics of HbA1c formation and removal, in order to better describe the relationship between HbA1c and BGC.22,23 However, while many of these models may possibly be theoretically sound to some extent, none so far have offered a practically-applicable dynamical approach to tracing the fluctuations of HbA1c over time, an approach that could result in application deployed in an SMBG device ensuring sufficient accuracy by sparse (e.g. fasting glucoses and occasional 7 points profiles) BG measurements.
Risk Analysis of Blood Glucose Data
The present inventors' group at the University of Virginia has also worked extensively on developing models of the relationship between SMBG and HbA1c. In an early study in T1D patients, we investigated how well the mean of SMBG data describes the actual mean BG.24 The linear formula HbA1c=5.21+0.39*BGMM (mean SMBG expressed in mmol/liter) resulted in a correlation of 0.7 between mean SMBG and HbA1c. Later, an updated linear relationship was derived: HbA1c=0.41046*BGMM+4.0775. However, due to a number of factors associated with routine SMBG, only about 50% of the variance of the actual BG was accounted for by mean SMBG. Thus, these findings suggested that mean SMBG was far from an ideal descriptor of actual average glycemia.
To correct for imperfections in SMBG sampling, we have introduced nonlinear corrections for the SMBG-based estimates of HbA1c, which used results from our theory of risk analysis of BG data25, namely the Low and High BG Indices (LBGI and HBGI). These nonlinear corrections resulted in improved numerical estimation of HbA1c from SMBG data and introduced mean absolute deviation (MAD) and mean absolute relative deviation (MARD) as measures of the accuracy of HbA1c estimation.26 This simple step was important for the understanding of HbA1c estimation because while correlation alone measures the strength of a linear association, it does not measure any possible offset of the estimates. For example, an estimate having two-fold higher values than actual HbA1c would have perfect correlation with HbA1c.
Further, based on our risk analysis theory, we introduced a method, system, and computer program, which was designed to aid the control in both T1 and T2 diabetic patients, by predicting from SMBG readings the long-term exposure to hyperglycemia, as well as the long-term and short-term risks for severe or moderate hypoglycemia.27 This approach used the HBGI and the LBGI, and later a new algorithm which derived an average daily risk range (ADRR)—a variability measure computed from routine SMBG data. We found that the ADRR provided a superior balance of sensitivity for predicting both hypoglycemia and hyperglycemia.28 
Most importantly for this presentation, we have conducted the largest to date study of the effects of offering real-time SMBG-based estimation of HBA1c, LBGI, and ADRR to patients with diabetes in their natural environment. In this study, 120 people with T1D used for 8-9 months a meter and a handheld computer providing these glycemic markers at each SMBG entry. As a result, average glycemic control was significantly improved, the incidence of severe hypoglycemia was reduced, and the patients rated highly the utility of the provided feedback.29 